Journal of Petrology | Volume 43 | Number 10 | Pages 1885-1908 | 2002
© Oxford University Press 2002
Dissolution of Corundum and Andalusite in H2O-Saturated Haplogranitic Melts at 800°C and 200 MPa: Constraints on Diffusivities and the Generation of Peraluminous Melts
ANTONIO ACOSTA-VIGIL*,,
DAVID LONDON,
THOMAS A. DEWERS and
GEORGE B. MORGAN, VI
SCHOOL OF GEOLOGY AND GEOPHYSICS, UNIVERSITY OF OKLAHOMA, NORMAN, OK 73019, USA
Received
February 28, 2001;
Revised typescript accepted
March 28, 2002
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ABSTRACT
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The mechanisms and kinetics of equilibration between peraluminous
minerals and granitic melt were investigated experimentally
by the dissolution of corundum and andalusite into H
2O-saturated
metaluminous haplogranitic melt at 800°C and 200 MPa. Mineral
and haplogranitic glass rods were juxtaposed inside platinum
capsules, and then subjected to experimental conditions for
times ranging from 12 to 2900 h. Upon melting, the mineral –melt
interface retreats with the square root of time. The composition
of the melt at the interface changes with time, but its ASI
[aluminum saturation index = molar Al
2O
3/(CaO + Na
2O + K
2O)]
remains constant at
1·20 after 480 h. This value is close
to the ASI of an H
2O-saturated haplogranitic melt in equilibrium
with corundum or andalusite, which may indicate that the composition
of the melt at the interface follows the liquidus of these minerals
in the system. Sodium and potassium diffuse rapidly uphill across
the entire length of the charge towards the interface, resulting
in a rapid and uniform increase in ASI throughout the entire
melt column. This uphill diffusion of alkalis is due to coupling
with excess aluminum entering the melt at the interface, and
involves long-range communication in the melt via chemical potential
gradients. The evolution of oxide concentration profiles with
time suggests that sodium, potassium, and a combination of aluminum
and alkalis constitute three directions in composition space
along which diffusion is uncoupled (eigenvectors) this system.
The aluminum–alkali eigenvector has a molar Al/(Na + K)
ratio of
1·20; its Na/K ratio, however, changes with
the composition of the liquid and with time as the entire melt
column approaches equilibrium. The solubility of H
2O shows a
positive correlation with the excess aluminum content of melt,
but conclusions about the stoichiometry of H
2O in the aluminum–
alkali eigenvector could not be obtained from our results. We
propose that some H
2O may provide charge balance for excess
aluminum. Multicomponent diffusion models yield eigenvalues
for the corresponding aluminum–alkali eigenvector of 0·3
x 10
-10 to 1·9
x 10
-10 cm
2/s. Calculated effective binary
diffusion coefficients for Al
2O
3 are higher, 1·0
x 10
-9 to 3·6
x 10
-9 cm
2/s. These diffusion coefficients are
used to calculate equilibration times between peraluminous minerals
and granitic melts in a model system in which two grains of
corundum or andalusite 1 cm apart are connected via a narrow
melt column. At the conditions of the experiments, diffusive
equilibrium through initially metaluminous H
2O-saturated melt
would be attained within
10
1–10
2 years. At H
2O activity
well below saturation of the melt, lower diffusivity of all
components may increase the time to equilibration to
10
4–10
5 years, approaching possible time frames for the generation and
extraction of crustal melts.
KEY WORDS: dissolution experiments; corundum; andalusite; haplogranite; chemical diffusion; ASI; peraluminous
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INTRODUCTION
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Diffusion is one of the main mass transport mechanisms in silicate
liquids, and it is the means by which magmas ultimately achieve
chemical and isotopic equilibrium. Because of this, diffusion
studies are essential in two ways. First, as noted by
Bowen (1921,
1928), the rate of diffusion is an important control
on whether or not equilibrium is reached during igneous processes
(e.g. partial melting, interaction between magmas and xenoliths,
mixing between magmas, and crystallization from a melt). Information
about diffusivity can, therefore, place constraints on the time
frame of these geological processes. Second, diffusion studies
can provide basic understanding of melt production at an atomic
scale by revealing likely melt species. The knowledge of speciation,
in turn, provides information on melt structure that is needed
to form a rigorous basis from which thermodynamic and transport
models for the melt can be constructed.
The partial melting of peraluminous protoliths should produce peraluminous melts in which the ASI [aluminum saturation index = molar Al2O3/(CaO + Na2O + K2O)] should have values >1 and should increase with rise in temperature as refractory peraluminous phases increasingly dominate the melting assemblage. Surprisingly, natural rock compositions and experimental results appear to contradict this expectation. Partial melts derived from the anatexis of strongly peraluminous protoliths can be metaluminous to weakly peraluminous, as for example at Ronda in the Betic Cordilleras of southeastern Spain, where tourmaline- and cordierite-bearing leucogranite dikes with a mean ASI value of 1·05 appear to be derived from strongly peraluminous migmatites (e.g. Torres-Roldán, 1983; Tubía, 1988; Acosta-Vigil et al., 2001). Published data (Fig. 1) suggest a broad negative correlation between ASI and temperature for experimental granitic melts and natural granitic leucosomes, which coexist with one or more strongly peraluminous phases (Weber et al., 1985; Wickham, 1987; Le Breton & Thompson, 1988; Vielzeuf & Holloway, 1988; Barbey et al., 1990; Patiño Douce & Johnston, 1991; Holtz et al., 1992a; Watt & Harley, 1993; Bea et al., 1994; Obata et al., 1994; Barbero et al., 1995; Gardien et al., 1995; Icenhower & London, 1995, 1996; Braun et al., 1996; Patiño Douce & Beard, 1996; Montel & Vielzeuf, 1997; Acosta, 1998; Patiño Douce & Harris, 1998). To explain the unexpected low ASI values of partial melts derived from very aluminous protoliths, we consider two hypotheses: (1) that the kinetics of dissolution of strongly peraluminous minerals is slow on the time scales of melt generation and extraction; (2) that the solubility of excess alumina in melt is a function of melt composition, i.e. the solubility of excess alumina is coupled in some way with the other components of the melt (e.g. Clemens & Wall, 1981; Patiño Douce, 1992; London et al., 2001). In this paper we experimentally investigate the mechanisms and kinetics of dissolution of corundum and andalusite into H2O-saturated metaluminous haplogranitic melt [the 200 MPa H2O-saturated minimum composition of Tuttle & Bowen (1958)] at 800°C, which is representative of crustal anatectic temperatures. We choose corundum because it is the alumina-saturating phase in (slightly) quartz-undersaturated melts (i.e. at temperatures above the liquidus surface of quartz), and andalusite because it is prevalent in siliceous S-type granitic rocks (e.g. Clarke et al., 1976; Kontak et al., 1984; Noble et al., 1984; Morgan et al., 1998). By ascertaining how, and how fast, metaluminous melts become peraluminous through reaction with these minerals, we can derive (1) an improved understanding of the speciation reactions in melt and, hence, the nature of the melt structural components, and (2) time frames for some geological processes that entail the melting of peraluminous minerals. A complementary study in progress assesses the effect of the compositional variables, in particular the activity of H2O, on the ASI of granitic melts (e.g. London et al., 2001).
In previous studies, Cooper & Kingery (1964), Samaddar et al. (1964) and Oishi et al. (1965) found that the dissolution of corundum is controlled by mass transport in the liquid phase. The experiments, however, entailed H2O-absent ceramic systems at 1300–1600°C and 1 atm. Schairer & Bowen (1955, 1956) defined a portion of the liquidus surfaces for corundum and mullite at 1 atm in the systems Na2O–Al2O3–SiO2 and K2O–Al2O3–SiO2, and from their work the ASI of the H2O-absent melt at corundum or mullite saturation is 1·05–1·15 for compositions closest to those of the haplogranite system. Holtz et al. (1992a, 1992b) and Joyce & Voigt (1994) experimentally investigated the solubility of mullite and sillimanite in the haplogranite system at elevated pressure. Although they did not provide complete details of melt compositions, their resultant glasses contained 1·9 ± 0·4 to 2·3 ± 0·3 wt % normative corundum, which corresponds to ASI values of 1·13–1·25.
The experiments reported here consist of the dissolution of corundum and andalusite into H2O-saturated metaluminous haplogranitic liquids at 800°C and 200 MPa. Concentration profiles perpendicular to the melting interfaces are used, in conjunction with multicomponent diffusion modeling, to infer both stoichiometry and transport properties of a new set of independently diffusing components. The new set of diffusing components provide clues about species in the melt, whereas the diffusivity data allow us to estimate rates of equilibration between melt and peraluminous minerals.
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MATERIALS AND METHODS
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Starting materials and experimental methods
The starting materials include gem-quality single andalusite
crystals from Minas Gerais, Brazil (Table
1); high-purity (99·8%)
and high-density (low-porosity) alumina ceramic rods from Vesuvius–McDanel
(part AXR128633004000-WJ42558)
1·6 mm in diameter, as
the corundum source; and synthetic anhydrous haplogranitic glass
from Corning Lab Services, New York (Table
1), fired from reagent-grade
powders at 1800°C and 1 atm to the normative composition
of the haplogranite minimum at 200 MPa H
2O (
Tuttle & Bowen, 1958).
Andalusite and haplogranitic glass rods,
1·7 mm
in diameter and 2–5 mm in length, were prepared using
a diamond core bit. Andalusite rods were cored perpendicular
to the
c-axis. Although the stable aluminosilicate phase at
the experimental temperature and pressure is sillimanite, we
used andalusite because we could not obtain sillimanite single
crystals of sufficient purity for this purpose. Andalusite,
however, showed no signs of reaction to sillimanite or mullite
in these experiments. The value of
G for the andalusite-to-sillimanite
reaction at the experimental conditions is very small [-260·06
J/mol, calculated from thermodynamic properties for andalusite
and sillimanite taken from
Robie et al. (1978) and
Holdaway & Mukhopadhyay (1993)]
and of the same order of magnitude
as the uncertainties for the measured thermodynamic properties
of both minerals. The alumina rod, consisting of an aggregate
of randomly oriented corundum microlites (grain size
20–50
µm), was cut perpendicular to its major axis in pieces
2 mm long. Before loading, rod faces were ground flat and polished
down to 0·3 µm using alumina abrasive.
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Table 1: Composition of the starting materials (in wt %); the anhydrous haplogranitic glass was also analyzed after hydration at 800°C and 200 MPa with different initial amounts of H2O
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Glass rods were juxtaposed against andalusite or alumina rods inside 1·8 mm i.d. platinum capsules, with 10–15 wt % deionized and ultrafiltered water added previously to ensure that all experiments were H2O saturated. In some runs, a small amount of gold powder (grain size 
5 µm) was added between the rods to mark the initial position of the mineral–melt interface and hence to allow calculation of dissolution rates. We also conducted experiments consisting of an 400 µm thick melt column sandwiched between two corundum rods. This shorter diffusion distance allowed the mineral–melt system to approach equilibrium via diffusion on a shorter time frame. Capsules were frozen before welding to prevent volatilization of added water. After welding, all capsules were heated to 100°C for 24 h to distribute H2O and test for leaks.
Experiments were performed in cold-seal reaction vessels inclined 15° from the horizontal. Capsules were placed with their long axes parallel to the vessels, such that the mineral–melt interfaces remained near vertical during the experiments. Runs were conducted at 800°C and 200 MPa for durations of 12–2900 h. The capsules were pressurized at room temperature, and then the temperature was raised to the experimental temperature in 20 min. Temperature was monitored with internal chromel–alumel thermocouples, and pressure was measured with a factory-calibrated Heise bourdon tube gauge. Variations of temperature and pressure with respect to the target values during the experiments were less than 2°C and 10 bars, respectively. Total temperature and pressure uncertainties are ±4°C and <10 MPa, respectively. Oxygen fugacity was controlled by the composition of the NIMONIC 105® vessels at 0·5 log units below the Ni–NiO buffer. Experiments were quenched using a jet of air plus water at a rate of 75°C/min. Capsules were weighed to check for leaks and then punctured to check for H2O saturation. Whole capsules were mounted in epoxy or Buehler TransopticTM thermal plastic, and polished perpendicular to the mineral–glass interface until the center of the cylinders was reached. Table 2 presents a list of all the experiments, specifying starting materials, initial amount of added water, and duration.
Analytical methods
The starting anhydrous glass, andalusite, and the experimental glasses, were analyzed with a Cameca SX-50 electron microprobe at the University of Oklahoma, using an accelerating voltage of 20 kV, a beam current of 2 nA, and a 20 µm fixed spot. Sodium, potassium and aluminum were concurrently analyzed first to minimize alkali volatilization and attendant changes in elemental ratios. Counting times were 30 s on peak for all elements, yielding calculated 3
minimum detection limits of 0·02 wt % for Na2O, K2O and Al2O3, and 0·05 wt % for SiO2. Based on counting statistics, analytical uncertainties are in the range of 0·5–1·0% for SiO2 and Al2O3, and 1·5–3·0% for Na2O and K2O, relative to their reported concentrations in glass. Morgan & London (1996) demonstrated that, under these analytical conditions, the loss of sodium and grow-in of aluminum and silicon intensities during analysis are negligible and comparable with or less than the analytical uncertainties, so that no corrections are needed. Thus, we have tabulated the H2O contents of quenched glasses based on the difference of the electron microprobe analysis (EMPA) totals from 100%. Morgan & London (1996) showed that, with the analytical conditions used here, the EMPA-difference method gives H2O contents within 1–10% relative of those obtained with Fourier-transform IR (FTIR) spectroscopy. The maximum uncertainty for the calculated ASI values is ±0·02. Anhydrous crystalline materials were used as standards: labradorite from the Stillwater complex (Montana) for aluminum, silicon and calcium; adularia from St. Gotthard (Switzerland) for potassium; and albite from Amelia County (Virginia) for sodium. Matrix reduction used the PAP correction algorithm (Pouchou & Pichoir, 1985).
In each experiment, three analytical transverses perpendicular to the mineral–glass interface were acquired: one at the center of the glass column and one within 300–400 µm of each edge. Three more transverses parallel to the mineral–glass interface were acquired at increasing distances of 30–100, 2000, and 3000–5000 µm. To analyze diffusion processes using mathematical models in one spatial dimension, it is important that diffusion takes place essentially along a direction perpendicular to the mineral–melt interface. We checked for this condition in two ways: (1) we studied in detail the composition of glass within 1000 µm of the interface in the 72, 480, and 960 h experiments, by conducting closely spaced (100–200 µm) analytical transverses parallel to the interface; (2) we examined the chemical zonation of the glass located close to the interface in the 960 and 2900 h experiments by X-ray mapping.
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RESULTS
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Concentration profiles: uphill diffusion of alkalis and changes in ASI
Concentration isopleths
Measured distributions of oxide components in the region of
glass close to the dissolution interface from the 72 and 480
h experiments show that concentration isopleths always are parallel
to the interface. The 960 h experiment, however, demonstrates
why a single centerline microprobe transverse is inadequate
to characterize the diffusion profiles. In this experiment,
the concentration isopleths curve and become perpendicular to
the mineral–melt interface near one edge of the charge.
X-ray images (Fig.
2) show that the curvature in the isopleths
is spatially associated with empty spaces between glass and
capsule, which were filled with H
2O vapor during the experiment.
This experiment reveals that diffusion of aluminum through the
vapor phase is much faster than through the melt volume. Our
EMPA of each sample as described above ensured that diffusion
from the edges of the melt column did not occur, or at least
did not influence the diffusion profile measured along the centerline
of the experiments.
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Fig. 2. X-ray maps of glasses in the 480 h (a–d), and 960 h (e–h) corundum dissolution experiments, in the region close to the corundum–glass interface. Corundum is always to the left of the glass, in white (a, e) or black (b–d, f–h). Black arrows indicate approximate directions of diffusion. White spots in (a) and (e) are vesicles filled with alumina abrasive.
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Concentration profiles
The compositions of the experimental glasses along analytical transverses perpendicular to the mineral–glass interface are summarized in Table 3, where the experiments are sorted by the dissolving mineral and the presence or absence of gold powder at the interface. Within each category listed in Table 3, experimental time increases from top to bottom. We chose three points along the transverses to present the compositions of the glasses: at 20–30 µm, 300 µm, and away from the interface. The compositions corresponding to ‘away from the interface’ represent mean values of those points located beyond the aluminum diffusion profile, where the concentration profiles are nearly flat (see below).
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Table 3: Compositions of the experimental glasses (wt %) along analytical transverses perpendicular to the mineral–glass interface
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In all experiments, the glass located close to the interface is characterized by a significant change from the starting composition; this portion of the glass will be referred to hereafter as the boundary layer. Beyond the boundary layer, the concentration profiles for all oxide components become essentially flat. Figures 3 and 4 show representative compositional profiles in the corundum dissolution experiments for three experimental times: short duration runs of 12–144 h, intermediate duration runs of 240–480 h, and long duration runs of 2160–2900 h. Comparable figures corresponding to the andalusite dissolution experiments can be downloaded from the Journal of Petrology web site at http://www.petrology.oupjournals.org. In all cases, the concentrations of aluminum, sodium and potassium are greatest at the interface and decrease away from it, whereas the concentration of silicon is least at the interface and increases away from it. Experiments of the shortest duration (12 h) yield glass cylinders that are fully and homogeneously hydrated (Fig. 5) but otherwise uniform in composition. Therefore, the melts become uniformly saturated in H2O before any measurable diffusion of other components commences. Estimated concentration profiles for H2O are flat for the corundum dissolution experiments of 12–144 h duration, whereas in 240–2900 h experiments H2O increases towards the interface, matching the profiles of aluminum and alkalis.
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Fig. 3. Composition of glasses in the corundum dissolution experiments, as a function of experimental time and distance to the corundum–glass interface. Each concentration profile represents the mean values of three analytical transverses perpendicular to the interface. In this and following figures, the compositions are given as obtained from the microprobe, and the dashed lines refer to concentrations in the starting H2O-saturated metaluminous melt.
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Fig. 4. Concentration of H2O, calculated by difference of the electron microprobe analysis totals from 100%, in the corundum experimental glasses, as a function of experimental time and distance to the interface. Each concentration profile represents the mean values of three analytical transverses perpendicular to the interface.
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Fig. 5. H2O concentration profiles of glasses in the 12 h corundum dissolution experiment, perpendicular (a–c) or parallel (d–f) to the interface.
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The concentration profiles of sodium and potassium indicate that alkalis diffuse against their own concentration gradients from bulk melt through the boundary layer to the dissolution interface. Furthermore, uphill diffusion of alkalis is very rapid and affects the entire melt reservoir. This is shown by the fact that, even in experiments of only 72 h duration with glass cylinders up to 5 mm long, concentration profiles for alkalis beyond the boundary layer are flat, and the ASI of the melt increases not only at the mineral–melt interface where aluminum is being incorporated, but also throughout the entire melt column as a result of loss of alkalis via diffusion towards the interface (Table 3, Fig. 6).
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Fig. 6. ASI of glasses in the corundum dissolution experiments, as a function of experimental time and distance to the mineral–glass interface. Each profile represents the mean values of three analytical transverses perpendicular to the interface. ASI of the starting H2O-saturated metaluminous melt is 1·00.
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At the mineral–melt interface the melt reaches an ASI of 1·20 in 480 h (Table 3, Fig. 6), and afterwards the ASI remains constant through time. The same melt ASI value of 1·20 was found by London et al. (2001) in experiments in which a large fraction of corundum or andalusite was equilibrated with a small fraction of H2O-saturated haplogranitic melt. This suggests that in these diffusion experiments with durations of 480 h or longer, the melt at the interface is in equilibrium with corundum or andalusite. Beyond the boundary layer, the ASI of the melt quickly (240 h) reaches a uniform value of 1·10 through the migration of alkalis to the boundary layer. With longer run times, the rate of increase in ASI declines and ASI increases only slightly with time up to run durations of 2900 h (Table 3).
Although Al/Si and Al/(Na + K) vary through the boundary layers as functions of position and run duration, it is notable that the molar Al/Na ratio is constant throughout the entirety of each diffusion profile; that is, the Al/Na ratio for a given experiment is the same everywhere in the melt (Fig. 7). This ratio increases steadily over the time frame of all experiments, as a result of the continuous supply of aluminum at the interface. The ratio Al/K also is uniform and increases with experimental time in the region of the melt beyond the boundary layer. Within the boundary layer, however, this ratio increases progressively towards the interface up to a maximum value of 3–3·25 (Table 3); this maximum value is reached in less than 72 h and is maintained over the time frame of all experiments. As a result, the experimental glasses are characterized by a uniform ASI throughout, except at the boundary layer where ASI increases progressively towards the mineral–melt interface.
Analysis of the 400 µm thick glass column sandwiched between two corundum rods along transverses perpendicular to the corundum–melt interfaces shows that the melt achieves a nearly uniform ASI of 1·21 (SD = 0·03) before the concentration gradients in silicon, aluminum and alkalis are erased (Table 3, Fig. 8).
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Fig. 8. Composition of glasses sandwiched between two corundum rods, along transverses perpendicular to the interfaces and after 10 (•) and 25 ( ) days of experimental time. Each concentration profile represents the mean values of three analytical transverses. The distance between the two interfaces is 390–410 µm.
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Increase in melt H2O concentration
After the metaluminous liquid becomes hydrated (in <12 h), H2O concentration progressively increases as the melt becomes increasingly aluminous, up to 20–30 wt % greater relative to the corresponding metaluminous melt (Table 3). This indicates that excess H2O from the capsule is still dissolving into the melt as a result of the compositional changes taking place in the liquid as the dissolution of excess aluminum proceeds. Previous studies have already shown that H2O solubility in granitic melts at 800–850°C and 200 MPa increases with decreasing normative quartz content and orthoclase/albite ratio (Holtz et al., 1995), and limited experimental evidence shows the same correlation with increasing excess alumina (Dingwell et al., 1984, 1997; Holtz et al., 1992a; Linnen et al., 1996; Behrens & Jantos, 2001). We compared the increase in H2O solubility with excess alumina (each on a moles/100 g basis) in the experimental glasses; although the degree of correlation is low (r = 0·4), in both the corundum and andalusite dissolution experiments the ratio of moles H2O/moles excess Al2O3 is similar and around eight (Fig. 9a). This ratio represents the slope of a regression line obtained by minimizing the deviations of the observations from the line in both the H2O and Al2O3 directions simultaneously (reduced major axis line, e.g. Davis, 1986). Scatter in the data arises in part from variations related to the calculation of H2O by difference (discussed above), and especially because the denominator (excess Al2O3) approaches zero, and hence crosses the analytical detection threshold, near the metaluminous compositions that form most of the data points. These results suggest a much greater influence of excess alumina on H2O solubility in melt than has been reported previously at these temperatures and pressures, where this ratio was found to vary between 0·1 and 1·4 (Fig. 9b). These new results, however, have to be considered with caution, as the correlation is very poor.
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Fig. 9. H2O vs excess Al2O3 concentrations in (a) glasses of the corundum dissolution experiments and (b) experimental H2O-saturated granitic glasses reported in previous studies. m refers to the slope of the lines fitted to the data.
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Composition changes at melt column boundaries
In contrast to other experimental studies on the diffusive dissolution of minerals (e.g. Zhang et al., 1989; Liang, 1999), the composition of the glass at the interface and throughout the melt column is not constant through time. At the interface, concentrations achieve minimum (silicon) or maximum (aluminum, sodium, potassium) values after 72–240 h, then inverting the trends with longer run times (Table 3). Away from the interface, aluminum and H2O increase whereas sodium and potassium decrease (Table 3). An important consequence of this behavior is that the glass does not strictly represent an infinite reservoir of the diffusing components.
Retreat of mineral–melt interface
The rate at which the corundum or andalusite interfaces retreat with melting provides information about the nature of the dissolution process (see the following section). We attempted to directly track the retreat of the interface by adding gold powder at the initial mineral–glass interface (Fig. 10a and b), and by calculations based on the final Al2O3/SiO2 ratio of the experimental glass (Fig. 10c). The results show that the dissolution rates are time dependent, and the interface retreats with the square root of time. The dissolution rates measured with gold powder, however, are greater than those calculated based on the concentration profiles by a factor of 25–30. To ascertain whether the gold powder or the calculations based on the profiles give the true dissolution rate, we measured under the microscope the length of the corundum rod before and after the experiment in the 48 and 240 h runs. We found no measurable change in the length of the rod, and hence the gold powder does not mark the original corundum–melt interface. As a final test, mass-balance calculations show that, if the distances between the gold particles and the mineral–melt interface represent corundum or andalusite dissolution distances, then the aluminum concentration in the glasses should be much higher than the measured values. We conclude that the gold particles moved away from the initial mineral–melt interface during either the experiment or quench, and that the calculations based on the chemical concentration profiles give a better approximation to the real dissolution rates.
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Fig. 10. Retreat of the corundum–melt and andalusite–melt interface with time, either measured with gold particles or calculated based on the alumina concentration profiles. The linear fits were forced to pass through the origin. The inset in (a) shows results from the 12 and 24 h experiments.
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DISCUSSION
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Dissolution of corundum and andalusite in H2O-saturated haplogranitic melts: interface reaction or diffusion in melt as rate-limiting processes
The dissolution of a mineral phase into a silicate melt that
is undersaturated in all or some components of the mineral initially
involves the detachment of components from the mineral surface
and their incorporation in melt. Once in melt, such components
can diffuse away from the mineral–melt interface with
or without reaction involving components originally present
in melt. Depending on the relative rates of these processes,
the dissolution rate of a mineral will be limited by reaction
at the interface or diffusion of components through the melt.
Concentration profiles in static (non-convecting) melt, therefore,
can be governed either by an interplay between interface reaction
rate and diffusion, or solely by diffusion rates through the
melt.
Reaction–diffusion models developed by Zhang et al. (1989) predict that dissolution of diopside (and possibly other silicates) becomes diffusion controlled and the melt interface composition reaches a constant or stationary saturation value in seconds. The diffusive mineral dissolution model developed by Liang (1999) predicts that the concentration profiles are independent of time when plotted against distance/time [the Boltzmann transformation discussed, for example, by Crank (1975)], and the composition of the melt at the interface is constant through time. In Liang’s formulation, the composition of melt at the interface depends on only the dissolution parameter 
, the initial composition of the melt and dissolving solid, and the diffusion coefficients. Both models (Zhang et al., 1989; Liang, 1999) consider the melt as an infinite reservoir whose composition far away from the interface remains constant through the interval of dissolution.
The results obtained in the present experiments indicate that convection did not play a role in the redistribution of components through the melt. This is supported by the regular concentration profiles in experimental glasses, and both the increase in thicknesses of the boundary layer and decrease in the dissolution rates of the minerals with increasing experimental time [compare with, for example, Watson (1982) and Shaw (2000)]. The observed retreat of the mineral–melt interface with the square root of time (Fig. 10) suggests that diffusion in melt was the rate-limiting process. When plotted as a function of distance/time, however, the concentration profiles do not overlap (Fig. 11). Moreover, the composition of the melt at the mineral–melt interface changes with time (Table 3).
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Fig. 11. Concentration of Al2O3 and Na2O vs distance to the mineral–glass interface normalized to the square root of time, in glasses of the corundum dissolution experiments.
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The contrasts between our experimental results and theoretical models by Zhang et al. (1989) and Liang (1999) indicate that either (1) dissolution of these minerals is not controlled uniquely by diffusion in the melt, and reaction at the interface also plays a significant role, or (2) dissolution is diffusion controlled but some of the premises considered in the theoretical studies do not hold for these experiments. If the rate of the interface reaction has some effect on the kinetics of mineral dissolution, one would expect the concentration of the mineral components in the melt at the interface either to remain constant or to increase with time. This is the case for the experiments up to 72–144 h, where the concentration of aluminum increases until it reaches a maximum value (Table 3). Shaw (2000) arrived at the same interpretation of quartz dissolution experiments in basanite melt, wherein the SiO2 concentration in the melt interface increased with experimental time. After 72–144 h, however, the concentration of aluminum in our experimental glasses at the interface decreases gradually with time. This approximately coincides with the establishment of equilibrium between the peraluminous minerals and the interface melt (see above). Although we conclude that diffusion in melt controls the concentration profiles from that point on, the change in composition at the interface and eventually throughout the entire melt column is a consequence of the finite nature of the melt reservoir together with the diffusion coupling between components derived from the dissolving mineral and melt. In the case of a finite melt reservoir, diffusion in the melt will persist until the concentration gradients for all components are erased and, therefore, those components that diffused uphill to couple with mineral components at the interface have to diffuse back towards the distant end of the melt column (Fig. 12). Because of this, the composition of the melt at the interface must change through time, and therefore the concentration profiles will not overlap when plotted against the normalized distance (distance/square root of time). The constant ASI of the interface melt at 1·20 shortly after the concentration of aluminum at the interface reaches a maximum value suggests that, from this point on, the composition of the boundary layer at the interface does lie along the corundum or andalusite saturation surface. Changes in composition follow from migration along that liquidus surface to the bulk composition where the tie line between the initial melt composition and corundum or andalusite crosses the liquidus surface for the relevant mineral.
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Fig. 12. Evolution of the composition of the glass through time in the corundum dissolution experiments, at the interface (1), at 300 µm from the interface (2), and beyond the boundary layer (3). The small numbers in italics refer to the duration of the experiments (only shown for the interface composition). Trajectory 1 shows how those components initially concentrated at the interface (aluminum and alkalis) diffuse back to the distant melt, with the composition of the interface melt tending towards the intercept between the 1·20 ASI line and the tie line joining initial melt and corundum. The constant ASI of the melt at 1·20 after 480 h suggests that the changes in composition from that point on follow from migration along the corundum liquidus surface. Trajectory 1 is initially dominated by the incorporation of aluminum from corundum and alkalis from the distant melt through  Na and K, and later by the migration of aluminum and alkalis towards the distant melt through Al. Trajectory 3 is due to the loss of alkalis to the interface through Na and K. Trajectory 2 is controlled for a short time by the loss of alkalis to the interface, and then by the arrival of aluminum and alkalis from the interface through Al. Although these experiments did not last long enough to observe the final stages of equilibration, we postulate that trajectories 2 and 3 would end as trajectory 1, turning towards the intersection between the 1·20 ASI line and the tie line joining initial melt and corundum, once the melt reaches an ASI of 1·20. From that point on, all the trajectories (compositional changes in the melt) would be controlled by the migration of aluminum and alkalis through Al. In that way, the melt would erase the concentration gradients while maintaining the 1·20 equilibrium ASI.
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We suggest that the previous mineral dissolution experimental studies (Zhang et al., 1989; Liang, 1999) were quenched before the limiting nature of the melt column length could influence the final development of the diffusion profile. Otherwise, the previous experiments are similar to those conducted here, wherein the boundary layer created by bi-directional diffusion of components would be erased over time, the composition at the mineral–melt interface would change over time, and the compositional profiles would become flat throughout the melt as the mineral and melt achieved chemical equilibrium. Short-duration mineral dissolution experiments are convenient tools for the extraction of diffusivities using analytical solutions for semi-infinite melt reservoirs, and only in those cases where uphill diffusion affects only that melt located close to the boundary layer, developing local troughs and humps in the concentration profiles (Fig. 13a). In cases like ours, however, where uphill diffusion involves migration along the entire melt column (Fig. 13b), information about the eigenvectors controlling the uphill diffusion will not be recovered with short-duration mineral dissolution experiments; it will only be recovered precisely with long-time diffusion experiments using analytical solutions for finite-melt reservoirs.
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Fig. 13. Two contrasting cases of uphill diffusion, involving either the melt region close to the boundary layer (a) or the entire melt reservoir (b). Dotted line indicates initial concentration of a given component in melt, and continuous line shows the concentration of this component after uphill diffusion. Shaded areas and dashed arrows indicate the melt region and direction, respectively, in which uphill diffusion takes place.
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Multicomponent diffusion
As the dissolution of corundum and andalusite into H2O-saturated haplogranitic melts seems to be a diffusion-controlled process at least in medium- to long-duration experiments, an understanding of the equilibration between crystals and melt requires an assessment of the multicomponent nature of diffusion in this system. The macroscopic quantitative treatment of chemical diffusion in multicomponent systems involves expressing the fluxes and concentrations of the diffusing components by N - 1 partial differential equations such as (1) and (2), respectively, with N being the number of chemical components in the system; these equations arise from mass conservation and a linear force-flux phenomenology (Fick’s law, e.g. Crank, 1975):
where
Ji and
Ci refer to the flux and concentration
of component
i, respectively,
t refers to time, and
Cj is the
concentration gradient of component
j. The flux and concentration
of the
Nth component is fixed by those of the other components
through closure.
Dij is the diffusion coefficient expressing
the proportionality between the flux of component
i and the
concentration gradient of component
j. The complete set of diffusion
coefficients relating fluxes and concentration gradients, arranged
in columns and rows, constitute the diffusion matrix [
D] that
characterizes the transport properties of the system. In a system
with
N components, [
D] will be an
N - 1 by
N - 1 matrix. Diffusion
coefficients relating the flux of a component to its own concentration
gradient (
Dij, where
i =
j) are referred to as diagonal terms
of the diffusion matrix; those relating the flux of a component
to the concentration gradient of other component (
Dij, where
i 
j) are referred to as off-diagonal terms. The matrix [
D],
however, is not unique for a given system at any given conditions;
it is only specific to the choice of solvent (the
Nth component)
and the chosen set of diffusing components and their stoichiometries
(e.g.
Zhang, 1993;
Chakraborty, 1995;
Liang et al., 1996;
Mungall et al., 1998).
Previous diffusion studies in silicate melts have already shown that the fluxes of the arbitrarily chosen oxide components (i.e. SiO2, Al2O3, etc.) rarely are independent of each other (e.g. Oishi et al., 1965; Cooper & Schut, 1980; Zhang et al., 1989; Wolf & London, 1994; Chakraborty et al., 1995a; Liang et al., 1996; Mungall et al., 1998; Shaw, 2000). Instead, they are coupled through the off-diagonal terms of the associated diffusion matrix [D]. A method of determining the stoichiometries of the components that diffuse independently of each other, along with values of their diffusivities, consists of finding the eigenvectors (i) and eigenvalues (
i) of the matrix [D] associated with the oxide components (e.g. Trial & Spera, 1994; Chakraborty, 1995; Mungall et al., 1998). The eigenvectors represent these ‘new’ diffusing components expressed as linear combinations of the ‘old’ oxide components; the eigenvalues correspond to the diffusion coefficients of these independent diffusing components. The eigenvectors, therefore, can be viewed as a new set of chemical components that have the virtue of uncouple chemical diffusion, meaning that the fluxes of these components proceeds independently of each other. Thus, in an N-component system, there will be N - 1 independent eigenvectors, and N - 1 eigenvalues. The orientation of the eigenvectors in composition space as well as the eigenvalues for a system at some given temperature and pressure conditions are independent of the choice of solvent or components and, therefore, are invariant properties of the system (e.g. Chakraborty et al., 1995b, and references therein; Liang et al., 1996; Mungall et al., 1998). The orientation of each eigenvector is given by N - 1 associated coefficients that express the relationships with respect to the oxide component reference frame. As the relative values of the N - 1 coefficients for each eigenvector are constant, the value of one of them can be fixed to be a constant number, e.g. unity. The arrangement of the eigenvector coefficients in columns results in another N - 1 by N - 1 matrix, [P]. Thus, Pij are coefficients of the [P] matrix and measure the participation of the oxide component i on the eigenvector j.
The nature of the independent diffusing components is investigated through diagonalization of [D]. As the diffusion matrix [D], however, is not known a priori for a given system and conditions, eigenvectors and eigenvalues have to be obtained from the oxide concentration profiles measured in the experimental glasses. That leads to a new set of N - 1 uncoupled partial differential diffusion equations, equivalent to (2), each of them expressing now the change in concentration of an independent diffusing component (i) with time as a function of its concentration gradient and its diffusion coefficient (i):
here
Ci refers to the concentration of the eigenvector
i. These partial
differential equations have to be solved with appropriate boundary
and initial conditions, and the analytical solutions are then
used to obtain eigenvectors and eigenvalues through a forward-modeling
approach in which the differences between calculated and experimental
concentration–distance–time data are minimized iteratively
(
Mungall et al., 1998). The function used to quantify such differences
is the
2 function (see
Trial & Spera, 1994;
Mungall et al., 1998). Thus, according to the multicomponent diffusion model
and using 6-oxygen molecular stoichiometry for the oxide components
and Si
3O
6 as the solvent, the equation relating the concentration
of Al
4O
6 to the eigenvectors and eigenvalues is the following
(e.g.
Zhang et al., 1989;
Mungall et al., 1998):
where
Ci(
) is the concentration of
i at distance
x from the interface and
at time
t,
Ci() refers to the initial concentration of component
i,
Ci() is the concentration of component
i at the interface,
Pij are coefficients of the [
P] matrix,
P-1ij are coefficients
of the inverse [
P] matrix, and C
j expresses the concentration
of the eigenvector
j at the given time and distance and for
a given eigenvalue
j.
The method described above, however, requires rigorous multivariate curve fitting techniques, and in our case does not yield unique results. This is due to the large number of unknown parameters: in the five-component system under investigation here, there are 16 unknowns—three coefficients for each of the four eigenvectors, plus four associated eigenvalues. Moreover, the mineral and melt compositions we used cover only one direction in compositional space, as the angle between the vectors corundum–melt and andalusite–melt is small. Trial & Spera (1994) showed that, for the magnitude of the uncertainties associated with electron microprobe analyses, it is possible to recover only some of the elements of the diffusion matrix from multiple (time series) experiments involving a single direction in composition space. Furthermore, that direction should not coincide with any eigenvector (Trial & Spera, 1994), or lie within a plane that contains two eigenvectors with associated eigenvalues of the same magnitude within measurement error (Mungall et al., 1998). Following Liang et al. (1996), an accurate estimate of the diffusion matrix in an N-component system requires diffusion experiments along at least N - 1 directions in composition space that cross at a given composition (that of interest) and are orthogonal to each other.
Despite these restrictions inherent to the system of interest here, in the next section we show how the concentration profiles and elemental covariations obtained from the dissolution of corundum or andalusite in H2O-saturated haplogranitic melt bear important information about transport properties in this system, specifically about the diffusing component controlling the migration of aluminum through the melt.
Analysis of concentration profiles: observations on relative component motion
Dissolution of corundum or andalusite into H2O-saturated haplogranitic melt does not simply consist of surface detachment and diffusion of the ‘quasicrystalline’ mineral components away from the mineral–melt interface, but involves the uphill diffusion of alkalis (Fig. 3). That guarantees that the direction in compositional space defined by corundum–melt or andalusite–melt pairs does not coincide with any eigenvector. Moreover, although the length scale of diffusion for all the oxide components might appear similar, the initial concentrations of alkalis change throughout the entire melt column well above the uncertainties associated with the microprobe analyses. This indicates that diffusion profiles are not binary and, therefore, that mineral–melt directions do not lie within a plane containing two eigenvectors with associated eigenvalues of the same magnitude.
In previous studies, uphill diffusion of alkalis and, in general, any other component in the melt, has been explained either by changes in activity coefficients with melt composition (e.g. Sato, 1975; Watson, 1982; Chekhmir & Epel’baum, 1991; Lesher, 1994; Shaw et al., 1998; Shaw, 1999) or as the result of coupled diffusion in multicomponent systems (Zhang et al., 1989; Chakraborty, 1995; Chakraborty et al., 1995a; Liang et al., 1996; Mungall et al., 1998, and references therein). The diffusion matrix [D] can be expressed as the product of two other matrices, [L] and [G]. The kinetic matrix [L] measures the effect of intrinsic mobilities and concentrations on the flux of diffusing components; the thermodynamic matrix [G] expresses the dependence of fluxes on the variation of chemical potentials—and therefore activity coefficients—with composition (e.g. Liang et al., 1997). Thus, the off-diagonal terms of [D] being different from zero, and therefore diffusion coupling, can be due to [L], [G], or both (e.g. Chakraborty et al., 1995a; Liang et al., 1996).
In the experiments presented here alkalis concentrate at the boundary layer, the region of the melt with the lowest silica and highest alumina concentrations. The local coordination of excess alumina in granitic melts is not yet clear (e.g. Lacy, 1963; Mysen et al., 1981b; Sato et al., 1991; Poe et al., 1992). Thus it is not obvious if the boundary layer melt is more or less polymerized than the distant melt, and therefore it is not clear if uphill diffusion of alkalis is due to partitioning between contacting melts as proposed by Watson (1982). The fact, however, that the flux of sodium through the melt is such that the molar Al/Na ratio is constant in the entire melt reservoir indicates that sodium (and possibly potassium) diffuses uphill in response to the flux of aluminum. It strongly suggests also that coupled diffusion is driven by the kinetic matrix [L], and that either aluminum and sodium activity coefficients do not vary with melt composition for the range of compositions found in our experiments, or they vary proportionally and in the same direction.
We propose, therefore, that an aluminum–alkali component may approximate one of the eigenvectors (Al) in this system at the temperature and pressure investigated. Diffusion along that direction in composition space would be responsible for the migration of aluminum and alkalis away from the interface in these experiments. The proportion of aluminum to sodium in this component is necessarily fixed by the aluminum to sodium ratio in the bulk melt, as shown in Fig. 7. That requires that this ratio will depend on the composition of the melt. The proportion of aluminum to potassium is such as to maintain an aluminum to total alkali molar ratio at 1·20, which is the ASI of an H2O-saturated haplogranitic melt in equilibrium with corundum or andalusite at the experimental temperature and pressure (London et al., 2001). This interpretation is suggested by experiments 171 and 172 (Table 3), in which the melt achieved a nearly uniform ASI of 1·20 before the concentration gradients in the oxide components were erased. As this is the equilibrium ASI of the melt, it is not likely to change from that point on during the redistribution of aluminum and alkalis through Al, implying that the direction of this eigenvector is along a constant ASI of 1·20.
Our results do not suggest any coupling of silicon with the rest of the oxide components. To test this, we compared analyzed silica concentrations in the 480 and 2900 h corundum dissolution experiments with theoretical values, calculated assuming that silica concentration is determined only by the migration of the other components. The theoretical concentrations are very close to the analytical values, suggesting to us that PSiAl, PSiNa, PSiK, and PSiH coefficients are close to zero, and that diffusion along the direction of the silicon eigenvector (Si) is much slower than along the directions of the other eigenvectors in the system; that is, Si < Na, K, Al, and H. This is not surprising, as in previous diffusion studies silica has always been found to constitute one of the slowest diffusing components (e.g. Watson, 1982; Baker, 1990). Our data, however, do not permit us to obtain the stoichiometry of Si.
Sodium and potassium diffuse through the bulk melt, faster than, and independently of, aluminum and silicon. This is indicated by the uphill diffusion of sodium and potassium towards the interface, the commensurate drop in their oxide concentrations in the glass beyond the boundary layer, between 7 and 12 wt % relative (Tables 1 and 3), and the small changes in the concentrations of alumina and silica beyond the boundary layer, between 1 and 3 wt %. In the case of alumina, the small increase in its concentration away from the interface can be explained by the migration of alkalis; in the case of silica, the changes are erratic but still very small. On the other hand, preliminary results of albite and K-feldspar dissolution experiments with the same starting glass and experimental conditions indicate that the fluxes of sodium and potassium are uncoupled (Acosta et al., 2000). We conclude that sodium and potassium, alone or with some exchange involving hydrogen (see below), may represent two directions in composition space along which diffusion is uncoupled, Na and K, respectively. Uphill diffusion of alkalis towards the interface would be accomplished along these directions.
The rapid hydration of the glasses without any noticeable diffusion of other components suggests that the eigenvector controlling the diffusion of hydrogen, H, is parallel to the H2O axis, and that the associated eigenvalue is one of the largest of the system. Our data also indicate that hydrogen might be coupled with other components. H2O concentration profiles, which generally increase towards the interface and match alumina profiles in the corundum experiments, give the appearance of uphill diffusion of this component and suggest coupling with aluminum. The increase in H2O solubility with excess aluminum in the melt may indicate that excess aluminum associates with H2O or its components in the melt and hence reduces its activity (e.g. London et al., 2001). We propose that some of the dissolved H2O dissociates to provide charge balance for the excess aluminum entering the melt that is not balanced by alkalis, and for the excess alumina created in the bulk melt that experiences alkali loss via diffusion. The H2O concentration profiles, therefore, could be the result of diffusion along more than one direction in composition space. The high uncertainty associated with H2O concentrations, however, does not permit us to infer the stoichiometry of H2O in these eigenvectors.
Extraction of diffusivities
The only component for which diffusivity can be assessed from these experiments is the aluminum–alkali component. Silica concentration profiles are dominated by diffusion of the rest of components, which provides only an upper limit for its diffusivity. In addition, although accomplished by diffusion along the sodium and potassium eigenvectors, uphill migration of alkalis is driven by the incorporation of aluminum into the melt at the interface; this provides only a minimum value for these diffusivities.
Diffusion along the direction of the aluminum–alkali eigenvector, however, will arguably control the equilibration between H2O-saturated haplogranitic melts and peraluminous minerals and, therefore, the diffusion coefficient or eigenvalue associated with this eigenvector will provide information about the kinetics of this equilibration. We calculated this diffusivity in two ways. First, we applied a multicomponent diffusion model using the forward-modeling approach described in the multicomponent diffusion section. Second, we calculated the effective binary diffusion coefficient (Cooper, 1968) associated with Al2O3.
Multicomponent diffusion modeling
The ideal analytical solution to the uncoupled differential diffusion equations that apply to our experimental results should be one taking into account the following: (1) the melt represents a finite reservoir; (2) the melt composition at the interface changes with time along the corundum–andalusite liquidus surface of the system; (3) the mineral–melt interface is not fixed but retreats with a velocity that is a function of time. None of the existing published solutions for mineral dissolution via diffusive transport, however, meet all of these conditions. As an approximation, we apply here two available solutions. First, one in which the melt reservoir is considered a semi-infinite medium, the mineral–melt interface is fixed, and the composition of the melt at the interface is constant through time (Crank, 1975):
where
Cj {x , } is the concentration of the eigenvector
j at distance
x from the interface and at time
t,
Cj {o } is the concentration
of
j at the interface, and erfc {
x} refers to the complementary
error function (= 1 - erf {
x}). The second solution, taken from
Smith et al. (1955), takes into account that the mineral–melt
interface retreats, although at a constant velocity
V:
Cj refers to the initial concentration of
j. Both
of these solutions also assume that diffusion takes place only
in one direction in space, that the diffusion coefficients do
not change with the composition of the melt, and that the changes
in the density of the melt with composition are negligible.
We checked the first assumption with closely spaced analytical
transverses and the X-ray raster mapping. The third assumption
was checked by calculation of the melt densities along the analytical
transverses perpendicular to the interface. Densities within
the boundary layer are equal to or up to 0·05 g/cm
3 higher
than those beyond the boundary layer,
2·27 g/cm
3; we
used for these calculations data from
Lange & Carmichael (1990),
Silver et al. (1990) and
Richet et al. (2000).
For both solutions we calculate the eigenvalue associated with the aluminum–alkali eigenvector for every experimental time equal to or greater than 240 h, using the composition of the melt at the interface at that time as the constant interface value, and the mean composition of the melt beyond the boundary layer as the starting melt composition. As in our experiments the mineral–melt interface retreats with the square root of time, the velocity of retreat at every experimental time is taken as the slope of the tangent to the function fitted to the experimental data at that time. To compare our results with previous ones we choose 6-oxygen molecular stoichiometry for the oxide components, Al4O6, Na12O6, K12O6, and H12O6, with Si3O6 as the solvent. According to the discussion in the previous section, some of the eigenvector coefficients are fixed (Table 4), and the only coefficients we let vary during the modeling are PHj and PiH. A Levenberg–Marquardt algorithm was used to calculate iteratively 2 for different sets of eigenvectors and diffusion coefficients until the 2 value was lower than an established threshold.
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Table 4: Eigenvectors (i ) coefficients deduced from analysis of the concentration profiles and referred to 6-oxygen oxide components with Si3O6 as solvent
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The diffusion coefficients for Al obtained with both solutions, together with the associated 2 values, are presented in Table 5. Figure 14 shows the fit obtained for the 2900 h experimental data. The main conclusions drawn from that modeling are the following. The best fits (lower 2 values) are always obtained when the eigenvalue for Al is around 1·0 x 10-10 cm2/s, independently of the values of PHj and PiH. The values found for this eigenvalue with both solutions and for all the experimental times are relatively close, so that the lowest and highest values are different by a factor of six. This observation supports our interpretation that mineral dissolution is diffusion controlled, at least after 240 h. Different sets of values for PHj and PiH yield adequate fits to the concentration profiles and, therefore, we cannot extract any unique information about diffusion of water from these experiments. The eigenvalues obtained for the rest of the eigenvectors are always similar to that for Al, reflecting that concentration profiles are mostly controlled by diffusion along the Al direction. They are not reported here as we think they are inaccurate representations of component diffusivities (as a result of system restrictions discussed above).
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ABSTRACT
INTRODUCTION
) and leucosomes and leucogranitic dikes in crustal anatectic terranes (
